A wave with a period of [tex]$1 / 3$[/tex] second has a frequency of
A) 3 Hz .
B) 300 Hz .
C) 33 Hz .
D) 67 Hz .
Answer (2)
The problem provides the period of a wave: T = 3 1 second.
Recall the relationship between frequency and period: f = T 1 .
Substitute the given period into the formula: f = 3 1 1 .
Calculate the frequency: f = 3 Hz . The answer is 3 Hz .
Explanation
Understanding the Problem We are given the period of a wave and asked to find its frequency. The period, denoted by T , is the time it takes for one complete cycle of the wave to occur. The frequency, denoted by f , is the number of cycles that occur per unit of time. The relationship between period and frequency is given by the formula: f = T 1 .
Applying the Formula We are given that the period of the wave is T = 3 1 second. We can substitute this value into the formula to find the frequency: f = 3 1 1 .
Calculating the Frequency To calculate the frequency, we simply take the reciprocal of the period: f = 3 1 1 = 3 Hz .
Final Answer Therefore, the frequency of the wave is 3 Hz. The correct answer is A.
Examples
Understanding the relationship between frequency and period is crucial in many real-world applications. For example, in music, the frequency of a sound wave determines the pitch of a note. A higher frequency corresponds to a higher pitch. In telecommunications, the frequency of a radio wave determines which station you are tuning into. In medical imaging, MRI machines use radio waves with specific frequencies to create detailed images of the human body. Knowing how frequency and period relate allows engineers and scientists to design and analyze these systems effectively.
The frequency of the wave, given a period of 3 1 second, is calculated to be 3 Hz using the formula f = T 1 . The correct answer is A) 3 Hz.
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